In that paper he came up with an estimate that the number of games of chess would be 10 That actually beats the number of atoms in the known universe which is estimated to be 10 78 to 10 82 atoms.
But how did Mr. Claude came up with the number 10 ? Well, the first thing Shannon did was to look at some games of chess. After some intense thinking, he noticed that on average, in any position, there are about 30 legal moves you can make. Take for this illustrative example below:. Black to move has 37 possibilities to choose from.
You can try it for yourself. Take any random position from any of your chess games and count how many legal moves each side has. It should be close around We now know that on average there are 30 legal moves each side can make. The counting of possible moves in chess is not a matter of knowing mathematics.
It is matter of "down to earth" feasibility. As you write, you seem surprised of not finding a mathemathian who knows what he is talking about that could give you a conclusive answer about the matter. Well, the best of them will always come with the answer. Why not a Bishop, or a Knight?
Most probably that person doing the counting will use a calculator otherwise he might be considered a rare human specimen with a rotten mind. I don't understand why is a calculator necessary to 'count' movies. Well, the answer to this question is very simple:. There are "sooooo" many possible positions in chess and it gets complex as the game moves forward.
The number which I gave above, describes the approximate number of possible moves in a chess game. Even though it looks small, that number is insanely HUGE. No kidding, it's larger than the number of particles in the universe. If you were to try and write that many dots down, there wouldn't be enough matter to make the pens. And even if you had enough pens to write it out, the paper and pens would be so condensed that it would form a giant black hole.
And the devil is well known to play chess usually with DEATH and while playing the fiddle so for some perfectly triffling and incorporeal payment I expect he would whisper the answer to you. Forums General Chess Discussion. Jan 31, 1. Jan 31, 2. Jan 31, 3. You don't need a math genius, because the answer is simple: A lot. Feb 1, 4. If you really want to blow your mind, calculate how many possible iterations of a chess game there are.
So, white can open up with 20 different first moves, and black can respond with 20 different first moves. That's 40 combinations after the first 2 moves, it starts adding up quick. Let us know what you come up with :. According to Shannons number it is 10 unique games of chess. Same moves in different order may lead to the same position. It must be pretty hard to give the exact number of legal positions, but there is a way of approximating it - generating random positions and counting how many were legal and how many not.
After you've generated and tested, say, a few milions, the percentage of illegal ones must be pretty close to the "absolute truth". Then you simply multiply it by the number of all possible positions. It's still an estimation, but reasonably accurate. This is exactly what is meant when people refer to "solving chess". If we are trying to find the number of ways of filling r positions with with n distinct objects, the equation we would use is n!
In the case of find the number of possible chess positions r is clearly 64, but n is a bit more difficult to find. The number i gave doen't account for pawn promotions, and some postions may not be legal, but it's a decent estimate.
Pawns are not distinct, for example if you get a position with doubled pawns it can be, say, either the e-pawn above the f-pawn or vice versa depending on how the position was reached, which we may have no way of knowing , but it's the same position Positions that emerge in real games, where both players tend to avoid doubled pawns , the number of reasonable positions is obviously a very tiny percentage of all legal positions. Naturally, pawns can also swap files due to captures say, b-pawn lands on the c-file and its comrade c-pawn on the b-file.
This would be a great challenge to come up with the exact correct answer. Ask God, He could tell you. Even a greater question who cares? There is not necessarily just one best move for any given position. Some positions are symetrical, so they would have at least two possible "best moves".
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